The final two Metaphysical Expositions argue that our original representation of space must be intuitive. I draw some surprising connections between Kant’s discussion and Leibniz’s account of the continuum. These connections indicate that the point of Kant’s analysis of <space> is to show that our original representation of space is infinitely complex in content. Since no discursive representation can be infinitely complex, our concept <space> cannot derive its content from discursive spontaneity. Its content must rather be given to the mind in order to be thought at all and thus originates in receptive intuition. Kant’s argument does not hinge on the singularity or holistic structure of space, as many hold, but on its infinite complexity and consequent givenness. I develop a novel account of the discursivity of conceptual representation that preserves the validity of Kant’s argument, defend Kant’s account of the infinity of space against prominent objections, and finally indicate how Kant’s argument entails the singularity of intuition (rather than presupposing it).

This chapter focuses on rhythmic and periodic patterns (RPPs). These are common EEG patterns found in critically ill patients. The variety of different types of patterns and their standardized naming conventions are described here. These patterns span from serving as markers of encephalopathy, to markers of seizure risk (interictal), to status epilepticus itself (ictal), and everything in between. This broad potential of diagnostic significance is known as the ictal–interictal injury continuum (IIIC). This chapter describes strategies for differentiating between more benign and more malignant RPPs. Basic management strategies for these IIIC patterns are also described in this chapter.

There are two Sun Tzu verses which, by Sun Tzu’s own affirmations, may be seen as summations of the active ingredient of his way of war. One is Theme #6’s centerpiece verse III.4 (Passage #6.1).

Two surveys of high-mass star formation (HMSF) are discussed. One is the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL), using the Atacama Pathfinder Experiment (APEX) 12 metre dish. The other uses the Institut de Radioastronomie Millimetrique (IRAM) Northern Extended Millimetre Array (NOEMA). The value of a representative survey of HMSFRs lies in learning what physical and chemical parameters are shared across a variety of sources. The results of statistically large samples of detected, or non-detected, sources such as that of ATLASGAL provide secure data from which to generalise about the typical star-formation process. The results of smaller but still multi-location studies such as the NOEMA sample give us greater specific details, albeit from a self-selecting sample, which may or may not be typical but that we can certainly say are common, at least until future wider surveys demonstrate error.

The three UCHII regions associated with the G34.26+0.15 high-mass star formation complex in Aquila are described, giving evidence for envelope infall, protostellar outflows, expanding ionized gas, and associated molecular hot core chemistry. The prototypical ‘cometary’ UCHII region ‘C’ in G34.26 is one focus, where the interface between ionized hydrogen (HII) and hot molecular core (HMC) gas is well observed and a rich hot core chemistry both detected and modelled in detail. Uncertainties in CH3CN formation, and the displacement of its peak emission from dust and NH3 peaks, are raised in relation to possible photodissociation in the hot core close to the UCHII-C feature.

In this chapter, basic concepts in fluid mechanics are introduced. Firstly, the definition of a fluid is discussed in depth with the conclusion that a fluid is such a substance that cannot generate internal shear stresses by static deformation alone. Secondly, some important properties of fluids are discussed, which includes viscosity of fluids, surface tension of liquids, equation of state for gases, compressibility of gases, and thermal conductivity of gases. Lastly, some important concepts in fluid mechanics are discussed, which includes the concept of continuum and forces in a fluid. Within these discussions, fluid is compared to solid in both microscopic and macroscopic to reveal the mechanism of its mechanical property. Viscosity of fluid is compared to friction and elasticity of solid to give readers a better idea how it works microscopically. Forces is classified as body force and surface force for further analysis. Finally, continuum hypothesis is introduced to deem the fluid as continuously separable, which tells the reader that fluid mechanics is a kind of macroscopic mechanics that conforms Newtonian mechanics and thermodynamics.

The book ends with the conclusions that the three categories of CFs analysed range on a continuum from compound-like to affix-like, and consist of an open class of elements destined to expand, to include novel splinters and form new words.

Brief overview of the importance and peculiarities of granular materials.

The subject here is the absorption coefficient, expressing the net power loss from the field over a unit path. At its heart is the line shape, which may be identified with the power spectral density function for fluctuations of the active dipole in the presence of an equilibrium bath of perturbers, and, as such, should satisfy the fluctuation–dissipation theorem. The more general properties of the absorption coefficient, which must reflect this balance, are first examined in some detail, particularly for the Van Vleck–Huber form. It is then shown that this, when expanded as a sum over individual lines, may be folded into more compact expressions. Outside the line core, these expressions must incorporate the fluctuation–dissipation theorem, and special attention is given to distinguish this case and that of the core itself, where it is of no consequence. Even the very general Fano theory does not, as it stands, satisfy the theorem, and can be used for the far-wing line shape only if these expressions are modified. Finally, some account is given of how they may be used with a molecular line database, and how a calculation of radiative transfer might proceed in the simplest of cases.

A long debate in the mechanicians' community was started by the seminal works by Piola, Mindlin, Rivlin, Toupin, Sedov and Germain. Higher gradient or microstructured continuum models have been questioned in several aspects. Sometimes they have been regarded as an empty mathematical "game" devoid of any physical application or, worse, they were considered to be inconsistent with the second principle of thermodynamics. Pantographic metamaterials, i.e. metamaterials having a multiscale pantographic microstructure, have been initially introduced in order to give an example of materials whose macroscopic continuous description must necessarily be given by a second gradient continuum model. Once 3D printing technology allowed for the realization of these microstructures it has been discovered that this class of metamaterials exhibits very interesting features, which may possibly lead to interesting technological applications.